Energy systems
Estimated battery-backed runtime
- where
- runtime (h)
- usable DC energy (Wh)
- inverter efficiency
- steady AC load (W)
Explain this equation
Estimates how long a battery and inverter can run a steady AC load. Use it for a first check on UPS or backup supply sizing.
E_DC is the usable DC energy in the battery, in watt-hours. η is the inverter efficiency as a decimal, covering energy lost converting DC to AC. P_load is the steady AC load in watts. t is the runtime in hours.
Multiplying stored energy by efficiency gives the energy delivered as AC, and dividing energy by power gives time. The ≈ is there because efficiency and battery capacity both vary with load and discharge rate.
1000 Wh at 90% efficiency feeding 100 W gives 9 hours. Double the load and the runtime halves; in practice it drops a little more, because batteries deliver less at high discharge rates.
Watch out: the answer is in hours, so multiply by 60 for minutes. Use usable energy, not nominal. For a real UPS, check the manufacturer's runtime data.
Multiply usable battery energy by conversion efficiency to estimate the AC energy available. Divide by the steady load to estimate hours of operation.
For an actual UPS, use the manufacturer runtime curve for the battery configuration and load. A simple energy calculation is useful for understanding the relationship, not guaranteeing autonomy.
Enter your values to see the result.
Common mistake
Using nominal energy when the question gives a smaller usable amount, or returning hours as minutes.
Limits
Ignores changing efficiency, idle consumption and discharge-rate effects unless included in supplied energy/efficiency. No guaranteed emergency-system runtime.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.